Question

A plane mirror and a concave mirror are arranged as shown in figure and $O$ is a point object. Find the position of the image formed after two reflections, first one taking place at the concave mirror.

• A. $50\text{cm}$ above $\text{A}$
• B. $100\text{cm}$ below $\text{A}$
• C. $100\text{cm}$ above $\text{A}$
• D. $50\text{cm}$ below $\text{A}$

Answer 1

The correct option is B $100\text{cm}$ below $\text{A}$

For first reflection at concave mirror,
object distance, $u=-110\text{cm}$,
focal length, $f=-\frac{R}{2}=-100\text{cm}$

From mirror formula,
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{110}=-\frac{1}{100}$

$\Rightarrow \frac{1}{v}=\frac{-1}{1100}$

$\Rightarrow v=-1100\text{cm}$

That means image $\left(I_1\right)$ will be formed $100\text{cm}$ behind the plane mirror.


$I_1$ will act as the (virtual) object for plane mirror. Since plane mirror is making ${45}^{\circ }$ with vertical axis, so a real image will form $100\text{cm}$ below the point $\text{A}$.

So, final image $\left(I_2\right)$ will be real and formed at a distance $100\text{cm}$ below point $\text{A}$.